The number 440
440 is a composite number with 16 divisors. Its prime factorisation is × 5 × 11. Divisors (16): 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 440: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.
- 2
440 is composite. Its prime factorisation is
- 3
The divisors add up to 1080; without 440 itself that is 640, so 440 is abundant (640 is more than 440). Euler's totient φ(440) = 160 numbers up to 440 share no factor with it.
- 4
The digits of 440 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 440 = 2^{3} \times 5 \times 11 \]440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 1080 |
| Euler totient φ(n) | 160 |
| Square | 193600 |
| Cube | 85184000 |
| Square root | 20.976177 (= 2√110) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 115 |
| Scientific notation | 4.4 × |
440 in other forms
| Form | Value |
|---|---|
| In words | four hundred and forty |
| Roman numerals | CDXL |
| Binary (base 2) | 110111000 |
| Octal (base 8) | 670 |
| Hexadecimal (base 16) | 1B8 |
| Base 3 | 121022 |
| As time | 440 seconds = 7 min 20 s |
Is 440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (440 ÷ 2 = 220) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (440 ÷ 4 = 110) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (440 ÷ 5 = 88) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (440 ÷ 8 = 55) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (440 ÷ 10 = 44) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (440 ÷ 11 = 40) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 440 a prime number?
No. 440 = × 5 × 11, so it is divisible by 2.
What are the factors of 440?
1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440.
What is 440 in binary?
110111000 (hexadecimal 1B8, octal 670).
What is the square root of 440?
About 20.9762, exactly 2√110.
What is 440 in Roman numerals?
CDXL.
Is 440 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 440?
440 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.